Spectrophotometric Measurement of Carbonate Ion in Seawater over a Decade: Dealing with Inconsistencies

The spectrophotometric methodology for carbonate ion determination in seawater was first published in 2008 and has been continuously evolving in terms of reagents and formulations. Although being fast, relatively simple, affordable, and potentially easy to implement in different platforms and facilities for discrete and autonomous observations, its use is not widespread in the ocean acidification community. This study uses a merged overdetermined CO2 system data set (carbonate ion, pH, and alkalinity) obtained from 2009 to 2020 to assess the differences among the five current approaches of the methodology through an internal consistency analysis and discussing the sources of uncertainty. Overall, the results show that none of the approaches meet the climate goal (± 1 % standard uncertainty) for ocean acidification studies for the whole carbonate ion content range in this study but usually fulfill the weather goal (± 10 % standard uncertainty). The inconsistencies observed among approaches compromise the consistency of data sets among regions and through time, highlighting the need for a validated standard operating procedure for spectrophotometric carbonate ion measurements as already available for the other measurable CO2 variables.

S3 Figure S1. Distribution of (A and D) in situ [CO 3 2-] (CO 3 2-; in µmolꞏkg -1 ), (B and E) in situ aragonite saturation (Ω aragonite ; dimensionless), and (C and F) in situ buffer factor (-ω DIC ; in mmolꞏkg -1 ) as a function of the TA to DIC ratio (TA/DIC). Upper panels show calculated variables from the global surface ocean (pressure < 200 dbar) DIC and TA data from GLODAPv2.2019. 5 Lower panels show the calculated variables from full water column pH and TA from the merged dataset in this study (Table 1). See Section 2.2 regarding thermodynamic CO 2 calculations. The z-axis shows salinity in color scale.

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Appendix B: Evolution of the methodology for measuring carbonate ion content.
The formation of lead carbonate (PbCO ) in seawater is given by: The formation (or stability) constant for PbCO , CO3 β 1 , refers to the equilibrium constant for the formation of PbCO in solution and is a measure of the strength of the interaction between Pb and [CO 3 2-] T to form PbCO . It is given by: where Pb represents the total amount of content of free Pb 2+ , Pb(II)-chloride species and minor amounts of Pb(II)-sulfate species. [CO 3 2-] T is the total amount of content of free and ionpaired carbonate and PbCO represents the total amount of content of Pb(II) complexed with carbonate, including contributions from mixed ligand species. All amounts of substance content are given in µmolꞏkg -1 of seawater.
When Pb(II) complexes with [CO 3 2-] T in Pb(II)-enriched seawater, the ultraviolet spectrum of the solution is affected and [CO 3 2-] T can be determined spectrophotometrically ([CO 3 2-] spec ) through Equation (1) in the main manuscript. This equation allows for the direct determination of [CO 3 2-] spec in terms of the ratio of Pb(II) absorbances of the sample at two given wavelengths (R value; Equation (2)), provided that the remaining terms in Equation (1) (log{ CO3 β 1 /e 2 }, e 1 , and e 3 /e 2 ) have been accurately characterized. Table S1 summarizes the main features of the five different approaches that have been described for the determination of [CO 3 2-] spec since 2008, as the methodology has been periodically revised, here abbreviated as BY08, 6 EAS13, 7 PAT15, 8 SHA17, 9 and SHA19. 10 Table S1 reports the different conditions at which the terms log{ CO3 β 1 /e 2 }, e 1 , and e 3 /e 2 in Equation (1) were characterized for each approach. In fact, the characterization of these terms is implicitly a calibration because it relates a given R value to a particular [CO 3 2-] T and, thus, the existence of various sets of calibration functions, one per approach, that yield five different [CO 3 2-] spec values from a single R measurement, is in practice equivalent to having five different methods for measuring [CO 3 2-] spec . In this regard, the five approaches overall followed the same fitting procedure for calibrating the spectrophotometric terms in Equation (1) that consists of making R measurements in seawater over a range of conditions (e.g., salinity and temperature) where the seawater has been independently analyzed for at least two of the usually measured CO 2 system parameters (e.g., pH, TA, and DIC). It is then possible to calculate a value for [CO 3 2-] T ([CO 3 2-] calc ) from the application of a given equilibrium model for seawater, taking account of all acidbase systems occurring in the sample, and seeking to fit the terms log{ CO3 β 1 /e 2 }, e 1 , and e 3 /e 2 as S5 functions of salinity and temperature. Table S2 summarizes the reported calibration functions for log{ CO3 β 1 /e 2 }, e 1 , and e 3 /e 2 in Equation (1) for each of the five approaches as a function of   salinity (BY08, EAS13, PAT15, and SHA17; all values referred to 25 ºC) and also temperature (SHA19). All formulations are referred to atmospheric pressure.
EAS13 reviewed the approach of BY08 using natural seawater samples and pH values measured spectrophotometrically with purified dye ( concentration in the cuvette with regard to former protocols (Table S1). Consequently, PAT15 proposed an additional correction for readjusting the measured R data (Equation (4)) because of the perturbation of the sample due to the Pb(II) reagent addition. PAT15 refitted the calibration functions (Table S2) (4)) was recommended. Instead, they reported an equation for correcting measured R as a function of a wavelength offset term (Equation (5)) ( Table 1). SHA17 also recharacterized the calibration functions (Table S2). Additionally, the authors recommended recording Pb(II) absorbances at wavelengths surrounding the primary target wavelengths (e.g., 233 nm, 234 nm, and 235 nm) because of the use of multi-wavelength measurement techniques in the future.
Finally, SHA19 reported the most recent review of the calibration functions. The authors did not change the procedure to obtain R 0 with regard to SHA17 (Table S2) but extended the characterization of the terms over a broader range of salinity and temperature to enable in situ observations by combining field datasets from former works with laboratory data (Table S1).  (2)). R 0 corresponds to the initial ratio before perturbation of the sample due to Pb(II) reagent addition for PAT15 (Equation (4)), and to the ratio corrected for wavelength offsets of the spectrophotometer for SHA17 and SHA19. Δλ 241.1 is the spectrophotometer-specific wavelength offset at λ = 241.10 nm, defined as the wavelength location of a holmium oxide standard absorbance peak as specified by the manufacturer minus the wavelength at which the spectrophotometer reports the peak, which causes a reversal in the sign of Equation (5) 3 2-] spec in seawater according to the five different approaches (Table S1). Each parameter is expressed with the general equation form of Z, following Sharp and Byrne. 10 The different approaches are denoted as BY08, 6 EAS13, 7 PAT15, 8 SHA17, 9 and SHA19. 10 S is salinity and t is temperature in ºC. Formulations by BY08, EAS13, PAT15, and SHA17 are referred to 25 ºC, being only salinity-dependent. The approach by SHA19 is also temperaturedependent (Table S1). All coefficients apply to a pressure of 1 atm.  Figure S2A). PAT15, SHA17, and SHA19 approaches return [CO 3 2-] spec values higher than BY08 for the whole R range, being larger than 10 % for [CO 3 2-] spec > 150 µmolꞏkg -1 (R < 0.46), particularly with the PAT15 approach ( Figure S2A).

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The first term in Equation (S4), 10 * 10 (in µmolꞏkg -1 ), is only marginally dependent on temperature when using SHA19 formulations, being mostly dependent on salinity for all the approaches (Table S2) and increases with it (inset in Figure S2B). This is directly linked to the presence of more carbonate ion content in higher salinity waters ( Figure S1). This first term in Equation (S4) is similar for BY08 and EAS13, with EAS13 being slightly lower ( Figure S2B). However, in PAT15, SHA17, and SHA19 the relation with salinity differs with regard to BY08 and also between them across the salinity range. Results among approaches are close between them at about ± 5 % only at salinity around 37 ± 1, except for SHA19.
This first term in Equation (S4) 10 * 10 is modulated upwards by and downwards by 1 * ( Figure S3). Regarding these two terms, the main changes in the evolution of the methodology relate to the term (upper row in Figure S3), which is related to higher carbonate ion content (lower R values), where more remarkable inconsistencies between spectrophotometric and calculated carbonate ion content have been found. [7][8][9][10]18 In this regard, the greatest changes were introduced by PAT15 and SHA19 ( Figure S3C and S3E) in low salinity waters, while SHA17 introduced the changes for high salinity waters ( Figure S3D).
The term 1 most strongly influences carbonate ion calculations at low carbonate content ( Figure S3F-J) and has slightly changed with regard to BY08 overall. PAT15 reported the same coefficients for this term, being SHA17 and SHA19 who introduced the greatest modifications compared to BY08. S11 Figure S2. Comparison of the methodology approaches by EAS13, PAT15, SHA17, and SHA19 (Table S1) Table S1 as a function of the absorbance ratio (R; Equation (2)) and salinity. The corresponding formulations are in The random uncertainty refers to the analytical precision of the measurements. SHA19 estimated it at ± 0.7 % (Table S1).
The systematic uncertainty refers to the uncertainty inherent to the fitting of the calibration functions (Table S2), which is based on [CO 3 2-] calc (Appendix B). This component of uncertainty can cause a bias in [CO 3 2-] spec due to the set of functions used. SHA19 estimated it at ±1.9 % in their approach.
The resulting combined (random plus systematic) total standard uncertainty assigned to [CO 3 2-] spec measurements amounts to ±2 % in SHA19, being consistent with previous approaches (Table S1). Hence, the total [CO 3 2-] spec standard uncertainty considers both the measurement imprecision and uncertainty inherent to the calibration functions.

Terminology relative to datasets description
In this study, dataset description applies to carbonate ion residuals shown in the results section.
Dispersion. Is a way of describing how scattered is a set of data. It refers to the variability or scatter of the data; when it is large, the data are widely scattered, while when it is small, S13 the data are clustered. Dispersion of data can be measured as the interquartile range (i.e. the difference between the 3 rd and the 1 st quartiles of the data; Figure 2) or as standard deviation (Table S4 and  ] calc residuals can be biased towards positive or negative values, within or beyond the ± 4 % limit for internal consistency.
The bias in carbonate ion residuals is related to the systematic component of [CO 3 2-] spec uncertainty, through the wavelength accuracy of the spectrophotometer used for measurement.

Terminology relative to measurement of absorbance
The spectrophotometer specifications (Table S3) impact the random and systematic components of [CO 3 2-] spec uncertainty, through the measurement of R (Equation (2)) values.  (Table S1) is also single beam.

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Isosbestic point. In this study, it refers to the particular wavelength, in nanometers (nm), at which Pb(II) absorbance spectra shows the same value of absorbance at different conditions (i.e., at different [CO 3 2-]). This is, the value of absorbance does not depend on [CO 3 2-].
Photometric accuracy. It marks the ability of the equipment to discern absorbance values within limits of confidence. It is a source of random uncertainty in R. A spectrophotometer with low photometric accuracy will introduce more random noise in R measurements, resulting in more dispersed R measurements. Table S3 shows the value of R random uncertainty for each spectrophotometer, according to their respective photometric accuracy.
Wavelength accuracy. It settles the capability of the equipment to read the absorbance at a given wavelength. It is a source of systematic uncertainty in R. This parameter can impact the accuracy of R measurements with regard to their true values and, thus, the goodness of the fitting of the set of functions (Table S2) due to the use of inaccurate R values. As reported in the Introduction and Appendix B, SAH17 proposed a correction to account for systematic offsets in R data (Equation (5)).
Wavelength repeatability. It is the stability of wavelength measurement. A measured wavelength should not drift within a range of wavelengths; it must be stable within a specified wavelength repeatability.

Stray light.
This parameter introduces an error in the recorded absorbance, leading to negative deviations in Beer-Lambert's Law, causing increasing deviations as absorbance increases. It affects the signal-to-noise ratio, causing increasing photometric underestimation as absorbance increases. It is a source of random uncertainty in R. 3 2-] calc estimation.

Appendix D. Δ[CO 3 2-] uncertainty assessment: uncertainty in [CO
As described in Section 2.2 in the main text, the five sets of calibration functions (Table S2) reported for the determination of [CO 3 2-] spec in seawater were assessed through the study of the magnitude and distribution of carbonate ion residuals (Δ[CO 3 2-] With regard to [CO 3 2-] calc in this study, the following remarks should be considered: 1-Differences in [CO 3 2-] calc obtained from either the pH-TA and DIC-TA input pairs are small (blue dots in Figure S4), showing absolute values with a mean and standard deviation of 1.9 µmolꞏkg -1 ± 1.5 µmolꞏkg -1 . As reported in the main text, all the results shown in this study were obtained with [CO 3 2-] calc from pH-TA.
2-The influence of the seawater model assumed for CO 2 system calculations, which relies on the different thermodynamic options for K 1 and K 2 , K HSO4 and TB constants assumed for calculating [CO 3 2-] calc , is small when the pH-TA input pair is considered, within 1 µmolꞏkg -1 (cyan dots in Figure S4). The two sets of thermodynamic constants tested with the CO2SYS package for MATLAB are (A) K 1 K 2 =10 (Lueker et al. 16 ) and K HSO4 = 3 (Dickson 14 and Lee et al. 17 ), and (B) K 1 K 2 = 4 (Mehrbach et al. 12 as refit by Dickson and Millero 13 ) and K HSO4 = 1 (Dickson 14 and Uppström 20 ). Only these two sets of functions were used since these were the sets of constants used to assess [CO 3 2-] calc in the five evolving approaches of the methodology, as shown in Table S1.

3-If [CO 3
2-] calc total uncertainty is reevaluated by readjusting measured pH values to pH values that would have been obtained using purified dye, according to Liu et al. 21 (data for Sigma Aldrich, in their Figure 2), it increases by 0.8 % -1.5 % over the [CO 3 2-] calc study range.
Hence, the use of unpurified dye for pH measurements in the merged dataset in this study is not relevant for the interpretation and discussion of the reported results. 3 2-] calc through using the software errors, from Orr et al., 22 is proportional to the concentration itself. It ranges between 2.5 µmolꞏkg -1 and 4.5 µmolꞏkg -1 for [CO 3 2-] calc obtained with the DIC-TA pair (black dots in Figure S4), and between 2.5 µmolꞏkg -1 and 8 µmolꞏkg -1 for the pH-TA pair (red dots in Figure S4) within the [CO 3 2-] calc study range (68 µmolꞏkg -1 -252 µmolꞏkg -1 ), so from 3.7 % to 1.8 % with DIC-TA and from 3.7 % to 3.2 % with pH-TA.  Table 1 in Orr et al. 22 for the constants].

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Mean Δ[CO 3 2-] and standard deviation for each cruise in this study are shown in Table S4 (for   the whole range of amount of [CO 3 2-] calc content) and    The random uncertainty inherent to the methodology for [CO 3 2 ] spec determination was tested with a Monte Carlo analysis. To examine the minimum random errors that could be ascribed to R measurements, the value of ±0.006 was selected to perform the corresponding perturbations, because it is the lowest value for R uncertainty derived from the respective photometric accuracy specifications of all spectrophotometers used in this study (Table S3). It derives from PE850 and SHI2600, in particular.
The Monte Carlo analysis modifies R measurements according to a random value from a normal distribution with a mean of zero and a standard deviation of 0.006/2. The perturbed R values are used with the EAS13 approach to obtain [CO 3 2 ] spec perturbed values that are used to calculate Δ[CO 3 2-]. Figure S5 shows